In this thesis the quasi free photo production of pion pairs on bound nucleons Gamma + A -->pi pi (A - 1) + Nis analyzed for liquid Deuterium. These measurements allow an isospin dependent determination of the mass differential and total cross section of pion pairs on Deuterium.In former experiments pion induced production of pion pairs was measured by the CHAOS and Crystal Ball collaborations. The invariant mass distributions showed a shift in strength towards the threshold region with increasing atomic number of the targets in case of the isoscalar pi pi meson system. According to theoretical predictions this effect could be interpreted as a positive signature of a partial restoration of chiral symmetry. As pions are strongly interacting particles, which get absorbed in the surface region of the nucleus, these measurements only probed small effective densities. In contrast, photons can penetrate the whole nucleus resulting in a higher effective nuclear density. A pioneering experiment with a photon beam was performed by the TAPS collaboration at the accelerator facility MAMI-B in Mainz in 1999. This measurement observed an invariant mass shift of the isoscalar pi0pi0 channel with increasing atomic number as well. In the pi± pi0 channel this effect was not observed which served as a cross check. This observation confirmed the former experiments, since final state interactions of the pions would affect in first order both isospin channels in a similar way. Due to the poor statistics, the significance of the data was however limited. The experiment described in this work reached a much higher statistical significance, allowing a review of the old data. In this experiment, the TAPS detector was used as a forward wall in combination with the Crystal Ball detector to achieve almost the complete 4pi solid angle coverage for particle detection at the MAMI accelerator facility. The installation of the experimental setup started at the end of 2003. The new readout electronics for the BaF2 crystals was used for the first time. Between June 2004 and April 2005 measurements on several targets were performed, including the lD2 data which has been analyzed in this work.The analysis of the Deuterium data is an essential contribution to understanding the ongoing processes for two reasons. Firstly, there is the possibility to compare the solid targets and Hydrogen to the lightest nucleus having Fermi motion included but the lowest possible nuclear volume, the Deuterium. For the second reason, there are no data for the mass differential cross section on the neutron available for the mentioned channels. Analyzing the Deuterium data and subtracting the published proton data, the cross section on the neutron gets accessible. An essential question for the theory is whether the cross section on neutron and proton are the same or how much they differ in the relevant energy regime. To determine the absolute cross section, the efficiency of the detector system is required. To provide this efficiency, I also developed the MonteCarlo simulation using a skeleton of the Crystal Ball simulation code, based on the GEANT package. Presently, BUU transport calculations can not describe the different behaviour in the isospin channels for the solid targets, which may partly be due to uncertainties in the production cross section on the neutron. Therefore, a final interpretation of the observed mass shift - whether it can be described by final state interaction alone or by a partial restoration of chiral symmetry - can not be made as yet. With the cross section determination on the neutron, the BUU calculations can be refined and compared to the analyzed data again. The cross section on the neutron shows a relative shift of strength towards lower m pi pi in comparison to the cross section on the proton. With the cross section on the neutron available, refined transport calculations should be performed.
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